The Atomic Trampoline Cavity

Abstract

Using an intense evanescent light wave as the lower mirror, and the gravitational force as the upper mirror, a vertical cavity for storing atoms can be constructed. Transverse confinement is obtained by totally internally reflecting the light off a concave as opposed to a planar crystal surface, which results in any atom reflected by the evanescent potential at a position away from the central axis receiving an impulse towards it. After a cursory discussion of atom optics and atomic cavities, we outline the configuration of the atomic trampoline cavity described above, and present analysis of the motion of atoms within it. A discussion of the classical dynamics and quantum modes in the cavity is given, together with other complicating factors which act as loss mechanisms out of the cavity. Various aspects of obtaining experimental realizations and applications of the cavity are considered. A detailed study of the quantum dynamics of atoms in the three dimensional cavity reveals that the dispersion can be adequately described in the transverse directions using a simulation involving a classical distribution of point-like atoms, where the probability density of finding an atom at a particular position in the simulation corresponds to the probability density of the atomic wavefunction. The classical simulations, however, significantly underestimate the spreading in the vertical direction. By calculating the modes of the atomic trampoline cavity, both in and out of the evanescent potential, the proportion of each of the modes in the excited state, and hence the decay rate, or linewidth due to spontaneous emission can be calculated. We found that even when the effect of the evanescent potential was included, the modes obtained correspond to those calculated by Wallis, Dalibard and Cohen-Tiennoudji [Appl. Phys. B 54,407 (1992)], who treated the bottom potential as infinitely steep and not exponentially decaying. In contrast to an optical Fabry-Pérot cavity, the linewidth was found to be strongly dependent on energy. Various other cavity parameters (finesse and Q) which depend on the loss due to spontaneous emission were also calculated. Using a ring cavity rather than a laser traveling wave to provide the light that totally internally reflects off the internal surface of the dielectric crystal, we can accumulate the phase change due to the single atom bouncing into and out of the evanescent wave and altering the refractive index of the cavity. A measurement of the phase of this light will reveal information about the atom. We found that the measurement did not significantly alter the mean or standard deviation of the atomic energy distribution across the modes of the cavity, as to first order the phase change of the light in the cavity is independent of the energy of the atom. The significant change in the energy distribution was the introduction of oscillations, which occurred when the phase measured was significantly different from the expected mean. The reason for these oscillations is that the measurement implies the weighting of modes just entering or leaving the evanescent wave should be increased or decreased. Ways of bringing this currently infeasible experiment closer to being achievable using novel design mechanisms are also discussed.